Last week, Andrew Neil set out to find the answer to the question that has vexed so many: why on earth aren't there more people like him? In his case, the query was serious. The former Sunday Times editor is now a presenter of political programmes put out at those low hours when no one is in the mood for politics – but, as we were told over and again in his BBC2 documentary, he's also among the last of a dying species: the ordinary boy done good. And good, he showed us, meant a pad in Chelsea, a housekeeper called Vanessa and a dining table so long you could rollerskate down the middle.

Neil is one of the "plain folk", as he put it, a member of the welfare-state-bred guerrilla army who once upon a time "steadily infiltrated the citadels of power". Others included Harold Wilson, who made the long trek from Yorkshire grammar school to Number 10, John Major and Alan Johnson.

This story about the golden age of social mobility in Britain is now a familiar one, and it has improved in the telling. Everyone knows Margaret Roberts was the daughter of a Grantham grocer; but it's usually forgotten that Mrs Thatcher's other half was a millionaire businessman.

In any case, the private-school boys and girls are now back. More than a third of MPs in the current Commons have been privately educated, a higher proportion than the 2005 batch, while eight government ministers went to Eton. Then there is the law, the media and the other plum white-collar sectors – all elite strongholds once more.

Yet for this chronic ailment, the Paisley Grammar boy prescribed exactly the same placebo as is on offer from the ministers he spent so long attacking. Meritocracy, he called it – and he would have struggled to find a frontbench politician of any party to dissent.

To the Westminster classes, meritocracy is nothing less than social alchemy. Take ability, add application, ensure the institutions play ball (schools and universities train like they should, employers don't discriminate) and bingo: the establishment becomes as porous as a Swiss cheese, accepting members based on ability rather than family estate. What's more, promise David Cameron and Nick Clegg, all this can be pulled off without the direct transfer of large amounts of cash from the wealthy to the rest. How magic is that?

A coalition of the centre-right is never going to applaud the argument that more social mobility can only be achieved with greater equality.

But there is another aspect to this story that is frequently missed by both politicians and pundits: it is that the elites in Britain and in America have changed. They now appear more open. More worldly. More meritocratic.

For a description of how that process works, look at a new book by Shamus Khan, a sociologist at Columbia University. For the writing of Privilege, Khan spent a year at an elite boarding school in New Hampshire. St Paul's charges $45,000 a year and has an endowment of $1m per pupil. Former presidential hopeful John Kerry was a student – at the same time as the current head of the FBI. In other words, this is the American Eton, the Yankee Harrow.

Boarding schools such as St Paul's used to be WASP-only territory. In Khan's telling, they were expressly designed to keep out Jews, black people and women from the political and social elite. Yet when the former alumnus went back, he found that around a third of the students were foreign or from ethnic minorities. And while a few old-school snobs still roamed the corridors, they were pretty isolated. Far more common was a child of a corporate lawyer or a banker.

These are children of the working rich, in other words, rather than the indolent aristocracy – just as Cameron and Clegg are sons of financiers. Kahn saw students learning not just about the Anglo-Saxon poem Beowulf but the Stephen King film, Jaws. St Paul's students are regularly flown in private jets to the opera in New York – then come back and listen to rap. In the academic jargon, they are cultural omnivores. Meanwhile, children from less privileged backgrounds get the rap without any opera.

Again, there are plenty of parallels with David "call me Dave" Cameron and his fondness for the Smiths, or Alexander Boris de Pfeffel Johnson's bicycling habit. This is an elite that looks modern and meritorious – while also having had privileges the other 90% of society couldn't dream of. It results in an elite version of meritocracy that is socially liberal and disdains racism and homophobia – while implementing economically conservative policies.

No wonder that, as Neil reports, a Downing Street debate on school-sports policy last year turned into a discussion of who played what position in the Eton wall game.

Yet as the Cambridge sociologist Diane Reay shows in her research, the working-class kids who do get into the good universities struggle to fit in. Here is Barbara, a history student at a post-92 university: "I keep thinking I shouldn't be here . . . I think it's in my head. I'm just doubting myself."

Compare that with another interviewee, a former public-school student Reay and her fellow academics call Will. "We know we are the great and the good, that's obvious," he says. "What's less clear is which of us are going to be the leaders among the front runners."

• The following correction was printed in the Guardian's Corrections and clarifications column, 3 February 2011. We declared the number of old Etonian ministers to be eight, that figure, supplied by the Sutton Trust, applied to the early days of the coalition. There are now nine old Etonians in the government, or 11 if whips without portfolio are included.